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Equation 1 · Part 8 · How Robotics and Embodied AI Actually Work

=

s^t+1=fθ(st,at),o^t+1∼pθ(o∣s^t+1)\hat{s}_{t+1} = f_\theta(s_t, a_t), \qquad \hat{o}_{t+1} \sim p_\theta(o \mid \hat{s}_{t+1})
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Dreamer-style world models learn a compact latent-dynamics model — a recurrent state-space model that predicts both a stochastic and a deterministic component of future latent state — and then train a policy by backpropagating through imagined rollouts inside that latent space, rather than through real or simulated environment steps directly [ 8 ] . DayDreamer took that specific mechanism, previously demonstrated mostly in video-game and simulated benchmarks, and applied it to physical robots learning online, without a simulator and without human demonstrations, reporting that four different physical robots (a quadruped and several manipulator arms) learned locomotion and manipulation skills…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.